Finite Group Databasebeta

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C₂₃×#3383 #15671002

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,27)(26,30,31,29)(32,33,37,40)(34,38,36,44)(35,42,43,46)(39,45,47,41);(24,26,28,31)(25,29,27,30)(32,34,37,36)(33,38,40,44)(35,41,43,45)(39,46,47,42);(32,35,37,43)(33,39,40,47)(34,41,36,45)(38,46,44,42);(24,27,28,25)(26,29,31,30)

Conjugacy classes & character table

805 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2115);